Downside Risk Aversion and the Downside Risk Premium

We search for a definition of the downside risk premium analogous to the Pratt-Arrow definition of the risk premium. However, even in the local analysis difficulties arise. To overcome these, we propose a definition based on the difference between two gambles. Further, a global analysis reveals that higher-order terms affect the downside risk premium and these cannot be ignored. We show that all five measures of the intensity of downside risk aversion that have been suggested are invalid in the case of the global analysis.